User blog:ThePerpetual/Hero's Path: Various Basic Spell Calculations
(Disclaimer): This blog is still a work in progress. I will finish it at a later time. It's occurred to me that just the basic spells in Hero's Path are probably some fairly impressive stuff, what with how some of them go and all They're generally supposed to be comparable to one another, but I'm fairly certain we'll have at least one major Outlier? We'll cross those bridges when we get there. Oh, and obviously I'm not exactly doing every category of spell, since that would be kinda, uh... redundant, probably? Ah well. As for general areas of effect for offensive spells? As I'd envisioned it, *"A meter or two" (Tier 1) *"Several meters" (Tier 2) *"Dozens of meters" (Tier 3) *"Hundreds of meters" (Tier 4) *"Thousands of meters" (Tier 5) *"Several kilometers" (Tier 6) And the range in each case is the next category up (save for Tier 1, which like Tier 2 is dozens of meters.) Need some space to use gigantic area of effect attacks, after all. As for Tier 6, the Ultima branch of offense magic, I'd just the range up one to dozens of kilometers I suppose? (shrug) Seems like the logical progression of that. Essentially, being able to toss around Fifth or Sixth Order Offensive Magic makes you a terrifying tactical nuke in the verse, and beings with that kind of firepower are feared within the verse for their ability to lay waste to the world around them. Fire Fire is pretty simple, it's just some basic fireball-type stuff The only statements I recall making regarding the actual intensity of the fire would be that Great Fire (Tier 3) is as hot as lava (~950 Celsius on average seems safe), and that Supra Fire (Tier 5) approaches the temperature of the surface of the Sun (~5600 Celsius: since it's "approaches", I'll use the slightly lower 5000 Celsius as a low-ball) *Flame's Mass: .3 kg/m^3 *Heat Capacity of Oxygen: 919 J/kg*K *Standard Temp. of Flame: 1200 C Which makes the first statement kinda pointless? Ah well Tier 1 *Volume of Sphere with Radius (1.5): 14.14 m^3 **Mass of Flame: (X * 0.3) = 4.24 kg *Potency: (4.24 kg * 919 * (1200 - 23)) = 4586251.1 Joules, or 0.0011 Tons of TNT. Wall level. Tier 2 *Volume of Sphere with Radius (5): 523.6 m^3 **Mass of Flame: (X * 0.3) = 157.08 kg *Potency: (157.08 kg * 919 * (1200 - 23)) = 169907624.0 Joules, or 0.041 Tons of TNT. Small Building level. Tier 3 *Volume of Sphere with Radius (24): 57905.84 m^3 **Mass of Flame: (X * 0.3) = 17371.75 kg *Potency: (17371.75 kg * 919 * (1200 - 23)) = 1.87904e+10 Joules, or 4.491 Tons of TNT. Large Building level. Tier 4 *Volume of Sphere with Radius (200): 3.35e+7 m^3 **Mass of Flame: (X * 0.3) = 1.005e+7 kg *Potency: (1.005e+7 kg * 919 * (1200 - 23)) = 1.08707e+13 Joules, or 2.598 Kilotons of TNT. Small Town level. Tier 5 *Volume of Sphere with Radius (2000): 3.35e+10 m^3 **Mass of Flame: (X * 0.3) = 1.005e+10 kg *Potency: (1.005e+10 kg * 919 * (5000 - 23)) = 4.59673e+16 Joules, or 10.986 Megatons of TNT. City level. Tier 6 *Volume of Sphere with Radius (5000): 5.24e+11 m^3 **Mass of Flame: (X * 0.3) = 1.572e+11 kg *Potency: (1.572e+11 kg * 919 * (5000 - 23)) = 7.19011e+17 Joules, or 171.848 Megatons of TNT. Mountain level. Ice Ice spells tend towards pretty "spikes" and such, with little flowery bits towards the edges and decorative pockets and gaps in the outer shell of the ice made, so something akin to a cone shape with a height of double the radius and 20% hollowness is about right here I think. All ice spells freeze water to a depth sufficient to support the weight of multiple squadrons of people: ten people, with a weight of about one ton total (counting gear and the like), would likely need ice of a thickness of 17.5 centimeters, or 0.175 meters. Anywho, let's get this on the road *Freezing Air into Ice: 566055.24 Joules/m^3 *Freezing Water into Ice: 418000000 Joules/m^3 Tier 1 *Volume of Cone with Radius (1.5), Double That Height, and 20% Hollowness: 5.656 m^3 *Volume of Ice Sheet with Radius (1.5) and 0.175 m Thickness: 1.24 m^3 *Potency: (566055.24 * X) + (418000000 * Y) = 521521608.4 Joules, or 0.1246 Tons of TNT. Small Building level. Tier 2 *Volume of Cone with Radius (5), Double That Height, and 20% Hollowness: 209.44 m^3 *Volume of Ice Sheet with Radius (5) and 0.175 m Thickness: 13.74 m^3 *Potency: (566055.24 * X) + (418000000 * Y) = 5.86187e+9 Joules, or 1.401 Tons of TNT. Building level+. Tier 3 *Volume of Cone with Radius (24), Double That Height, and 20% Hollowness: 23162.336 m^3 *Volume of Ice Sheet with Radius (24) and 0.175 m Thickness: 316.67 m^3 *Potency: (566055.24 * X) + (418000000 * Y) = 1.45479e+11 Joules, or 34.77 Tons of TNT. City Block level. Tier 4 *Volume of Cone with Radius (200), Double That Height, and 20% Hollowness: 1.344e+7 m^3 *Volume of Ice Sheet with Radius (200) and 0.175 m Thickness: 21991.15 m^3 *Potency: (566055.24 * X) + (418000000 * Y) = 1.68001e+14 Joules, or 40.153 Kilotons of TNT. Town level. Tier 5 *Volume of Cone with Radius (2000), Double That Height, and 20% Hollowness: 1.344e+10 m^3 *Volume of Ice Sheet with Radius (2000) and 0.175 m Thickness: 2199115 m^3 *Potency: (566055.24 * X) + (418000000 * Y) = 8.52701e+15 Joules, or 2.038 Megatons of TNT. Small City level. Tier 6 *Volume of Cone with Radius (5000), Double That Height, and 20% Hollowness: 2.096e+11 m^3 *Volume of Ice Sheet with Radius (5000) and 0.175 m Thickness: 1.37e+7 m^3 *Potency: (566055.24 * X) + (418000000 * Y) = 1.24372e+17 Joules, or 29.726 Megatons of TNT. City level. Big, tall ice is quite stronk Lightning Lightning is a bit different in that it's not exactly filling an area with "lightning energy", usually, so much as calling lightning strikes from the sky that proceed to do so on their own. Used indoors, said strike simply doesn't manifest until it would reach through the ceiling. Lightning math is somewhat tricky, but to my understanding (based on these two calcs), the energy value for a larger than usual/sustained bolt of lightning equals: (9.55e+8 A/m^2 * A) * 1.0e+9 * T = E Where *A = the surface area the bolt strikes, in square meters (m^2), *T = the time the bolt lasts, in seconds (for a normal bolt of lightning, this is 0.000051 seconds, or 5.1e-5 seconds), and *E = the final energy yield in joules. Tier 1 Really, super easy- it's just a lightning bolt (1 billion Joules) that also has magical properties and charges a small area with a burst of lightning. Potency: 1.0e+9 Joules, or 0.239 Tons of TNT. Small Building level+. Tier 2 "An array of lightning strikes" Since the previous burst was 1.5 meters in radius, or 7.07 square meters in area: and, I imagine at least, a good half of the area is entirely engulfed in bursts of electric energy in this way: in other words, Lightning spells throw one bolt per (7.07 * 2 =) 14.14 square meters of area they cover, plus one for the center for good measure. Area of Circle w/ Radius of 5 meters: 78.54 meters, /14.14 = 5. Plus one is six bolts, so Potency: 6.0e+9 Joules, or 1.434 Tons of TNT. Building level+. Tier 3 "An array of lightning strikes, followed by a singular central strike that bellows forth an engulfing wave of electrical energy" I imagine the central bolt's almost certainly bigger and badder than a mundane bolt, if it's exploding like that, but how much so? I'd written a little mini-story, once upon a time, where a big lightning spell was used to engulf a human-like Qliphoth Lord in a torrent of lightning. I don't see these lightning spells as being a "prolonged bolt" in that same way: continuous, visible streams are more demonstrative in fiction (and real life, for that matter) of a more powerful lightning user, and so for now I'll not tinker with the timeframe: though, the surface area? The width of an average human male is 0.2105 meters, and the area of a circle with that radius would be 0.1392 m^2. The area of the spell on the whole is 1809.56 m^2, which means (/14.14 =) 127 bolts. Then, the central bolt = (9.55e+8 * 0.1392 m^2) * 1.0e+9 * 5.1e-5 = 6.77974e+12 Joules. Potency: 6.77974e+12 + (1.0e+9 * 127) = 6.90674e+12 Joules, or 1.651 Kilotons of TNT. Small Town level. Tier 4 In addition to accounting for a bigger area-of-effect for the overall spell, the bolt's size increases substantially with each tier-up from here. Doubling in radius seems somewhat stingy given the much more drastic increases in area-of-effect, so I will roll with it for now. Area of 200 meter Circle: 125664 m^2, / 14.14 = 8887 bolts Bolt Radius of (0.2405 * 2 =) 0.411 meters, and thus Area of 0.5307 m^2 Central bolt = (9.55e+8 * 0.5307 m^2) * 1.0e+9 * 5.1e-5 = 2.58477e+13 Joules. Potency: 2.58477e+13 + (1.0e+9 * 8887) = 3.47347e+13 Joules, or 8.302 Kilotons of TNT. Town level. Tier 5 Area of 2000 meter Circle: 12566400 m^2, /14.14 = 888712 bolts Bolt Radius of (0.2405 * 2^2 =) 0.822 meters, and thus Area of 2.1227 m^2 Central bolt = (9.55e+8 * 2.1227 m^2) * 1.0e+9 * 5.1e-5 = 1.03386e+14 Joules. Potency: 1.03386e+14 + (1.0e+9 * 888712) = 9.92098e+14 Joules, or 237.117 Kilotons of TNT. Large Town level. Tier 6 Area of 5000 meter Circle: 78539800 m^2, /14.14 = 5554441 bolts Bolt Radius of (0.2405 * 2^3 =) 1.644 meters, and thus Area of 8.4909 m^2 Central bolt = (9.55e+8 * 8.4909 m^2) * 1.0e+9 * 5.1e-5 = 4.13549e+14 Joules. Potency: 4.13549e+14 * (1.0e+9 * 5554441) = 5.96979e+15 Joules, or 1.427 Megatons of TNT. Small City level. I could almost definitely get far larger results if the center bolts lasted for any kind of significant timeframe, but between the lack of solid conception for these spells and the really silly potential inflation that would allow for, I think that's the most I'll implement of lightning math for a while. Earth Tier 1 Tier 2 Tier 3 Tier 4 Tier 5 Tier 6 Holy While holy attacks don't behave like true light, when not suppressed they have a tendency to shine "like the Sun". I didn't exactly establish exact parameters for from how far away is the big problem, but I can probably assume that it shines like the Sun (apparent magnitude: -26.8) from past the edge of its area of effect, in each case. About double the edge of the area of effect seems about right. Tier 1 *Distance to App. Lum. -26.8: (((1 + 2)/2) * 2) = 3 meters *Potency: 1.4945e-4 Gigawatts, or 149450 Joules per second. Wall level. Tier 2 *Distance to App. Lum. -26.8: (5 * 2) = 10 meters *Potency: 1.6606e-3 Gigawatts, or 1660600 Joules per second. Wall level. Tier 3 *Distance to App. Lum. -26.8: ((12 * 2) * 2) = 48 meters *Potency: 0.03826 Gigawatts, or 38260000 Joules per second, or ~0.0091 Tons of TNT. Small Building level. Tier 4 *Distance to App. Lum. -26.8: ((100 * 2) * 2) = 400 meters *Potency: 2.657 Gigawatts, or 2.657e+9 Joules per second, or 0.635 Tons of TNT. Building level. Tier 5 *Distance to App. Lum. -26.8: ((1000 * 2) * 2) = 4000 meters *Potency: 265.7 Gigawatts, or 2.657e+11 Joules per second, or 63.5 Tons of TNT. City Block level+. Tier 6 *Distance to App. Lum. -26.8: (5000 * 2) = 10000 meters *Potency: 1660.6 Gigawatts, or 1.6606e+12 Joules per second, or 396.89 Tons of TNT. Multi-City Block level. Well, then. Holy doesn't do well with calcs, it would seem. Zie And of course, there is the non-elemental spell, Zie. Unlike it's more mundane kin, Zie as a non-elemental spell dissolves matter it destroys into its mere component animating pieces, rather than simply damaging and destroying matter in the more mundane way that other elemental attacks do- while I'm pretty certain that E = mc^2 doesn't apply here, I believe atomization does: being capable of reducing living flesh at minimum to such component pieces within a spherical area of effect is probably potent. *Atomization of Human Body: 72416.33 Joules/cubic centimeter Without further ado, Tier 1 *Volume of Sphere (with radius 150 in cm): 1.41e+7 cm^3 *Potency: 1.02107e+12 Joules, or 244.04 Tons of TNT. Multi-City Block level. Tier 2 *Volume of Sphere (with radius 500 in cm): 5.24e+8 cm^3 *Potency: 3.7946e+13 Joules, or 9.069 Kilotons of TNT. Town level. Tier 3 *Volume of Sphere (with radius 2400 in cm): 5.79e+10 cm^3 *Potency: 4.19291e+15 Joules, or 1.002 Megatons of TNT. Small City level. Tier 4 *Volume of Sphere (with radius 20000 in cm): 3.35e+13 cm^3 *Potency: 2.42595e+18 Joules, or 579.82 Megatons of TNT. Mountain level+. Tier 5 *Volume of Sphere (with radius 200000 in cm): 3.35e+16 cm^3 *Potency: 2.42595e+21 Joules, or 579.82 Gigatons of TNT. Large Island level+. Tier 6 *Volume of Sphere (with radius 500000 in cm): 5.24e+17 cm^3 *Potency: 3.79462e+22 Joules, or 9.069 Teratons of TNT. Country level. Yeah, that's about what I had thought. For what it's worth? Vaporization wouldn't yield much lower than this: titanium's value of 49079.7 J/cc, for example, would essentially just reduce these results to two-thirds their current value. That said, with Zie being harder to learn/taking more mana to cast, it's easy to justify this result being separate from the rest. Yields *'Tier 1 Magic:' Up to 0.239 Tons of TNT *'Tier 2 Magic:' Up to 1.434 Tons of TNT *'Tier 3 Magic:' Up to 1.651 Kilotons of TNT *'Tier 4 Magic:' Up to 40.153 Kilotons of TNT *'Tier 5 Magic:' Up to 10.986 Megatons of TNT *'Tier 6 Magic:' Up to 171.848 Megatons of TNT Category:Blog posts Category:Calculations Category:The Ultimaverse Category:Hero's Path